相关论文: Nearly optimal codebooks based on generalized Jaco…
Codebooks with small maximum cross-correlation amplitudes are used to distinguish the signals from different users in CDMA communication systems. In this paper, we first study the Jacobi sums over Galois rings of arbitrary characteristics…
Codebooks are required to have small inner-product correlation in many practical applications, such as direct spread code division multiple access communications, space-time codes and compressed sensing. In general, it is difficult to…
Codebooks with small inner-product correlation have application in unitary space-time modulations, multiple description coding over erasure channels, direct spread code division multiple access communications, compressed sensing, and coding…
In this paper, using additive characters of finite field, we find a codebook which is equivalent to the measurement matrix in [20]. The advantage of our construction is that it can be generalized naturally to construct the other five…
In this paper, we present explicit description on the additive characters, multiplicative characters and Gauss sums over a local ring. As an application, based on the additive characters and multiplicative characters satisfying certain…
In this paper, we present two new constructions of complex codebooks with multiplicative characters, additive characters and trace functions over finite fields, and determine the maximal cross-correlation amplitude of these codebooks. We…
Codes in the sum-rank metric have received many attentions in recent years, since they have wide applications in the multishot network coding, the space-time coding and the distributed storage. In this paper, by constructing covering codes…
Constructions of distance-optimal codes and quasi-perfect codes are challenging problems and have attracted many attentions. In this paper, we give the following three results. 1) If $\lambda|q^{sm}-1$ and $\lambda…
Nearly perfect packing codes are those codes that meet the Johnson upper bound on the size of error-correcting codes. This bound is an improvement to the sphere-packing bound. A related bound for covering codes is known as the van Wee…
We address the question of constructing explicitly quasi-uniform codes from groups. We determine the size of the codebook, the alphabet and the minimum distance as a function of the corresponding group, both for abelian and some nonabelian…
We employ signed measures that are positive definite up to certain degrees to establish Levenshtein-type upper bounds on the cardinality of codes with given minimum and maximum distances, and universal lower bounds on the potential energy…
We consider matrices on infinite trees which are universal covers of Jacobi matrices on finite graphs. We are interested in the question of the existence of sequences of finite covers whose normalized eigenvalue counting measures converge…
Variational inequalities represent a broad class of problems, including minimization and min-max problems, commonly found in machine learning. Existing second-order and high-order methods for variational inequalities require precise…
Quasi-logarithmic combinatorial structures are a class of decomposable combinatorial structures which extend the logarithmic class considered by Arratia, Barbour and Tavar\'{e} (2003). In order to obtain asymptotic approximations to their…
In this paper, we introduce the notion of the complete joint Jacobi polynomial of two linear codes of length $n$ over $\mathbb{F}_q$ and $\mathbb{Z}_k$. We give the MacWilliams type identity for the complete joint Jacobi polynomials of…
Hybrid character sums are an important class of exponential sums which have nice applications in coding theory and sequence design. Let $\gf_{p^m}$ be the finite field with $p^m$ elements for a prime $p$ and a positive integer $m$. Let…
We consider the integration of two-dimensional, piecewise constant functions with respect to copulas. By drawing a connection to linear assignment problems, we can give optimal upper and lower bounds for such integrals and construct the…
We apply the methods of classical approximation theory (extreme properties of polynomials) to study the essential support $\Sigma_{ac}$ of the absolutely continuous spectrum of Jacobi matrices. First, we prove an upper bound on the measure…
Jacobi's results on the computation of the order and of the normal forms of a differential system are translated in the formalism of differential algebra. In the quasi-regular case, we give complete proofs according to Jacobi's arguments.…
In this paper we study spread codes: a family of constant-dimension codes for random linear network coding. In other words, the codewords are full-rank matrices of size (k x n) with entries in a finite field F_q. Spread codes are a family…